Subject description - B0B01MA1

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B0B01MA1 Mathematical Analysis 1
Roles:P Extent of teaching:4P+2S
Department:13101 Language of teaching:CS
Guarantors:Tkadlec J. Completion:Z,ZK
Lecturers:Tkadlec J., Velebil J. Credits:7
Tutors:Dvořák J., Sobotíková V., Tkadlec J., Velebil J. Semester:Z,L

Web page:

https://moodle.fel.cvut.cz/courses/B0B01MA1

Anotation:

The aim of the course is to introduce students to basics of differential and integral calculus of functions of one variable.

Study targets:

The aim of the course is to introduce students to basics of differential and integral calculus of functions of one variable.

Course outlines:

1. Real numbers. Elementary functions.
2. Limit and continuity of functions.
3. Derivative of functions, its properties and applications.
4. Mean value theorem. L'Hospital's rule, Taylor polynomial.
5. Local and global extrema and graphing functions.
6. Indefinite integral, basic integration methods.
7. Integration of rational and other types of functions.
8. Definite integral (using sums). Newton-Leibniz formula.
9. Improper integral. Application of integrals.
10. Sequences and their limits.
11. Rows, criteria of convergence.
12. Introduction to differential equations.
13. Other topics of mathematical analysis.

Exercises outline:

1. Real numbers. Elementary functions.
2. Limit and continuity of functions.
3. Derivative of functions, its properties and applications.
4. Mean value theorem. L'Hospital's rule, Taylor polynomial.
5. Local and global extrema and graphing functions.
6. Indefinite integral, basic integration methods.
7. Integration of rational and other types of functions.
8. Definite integral (using sums). Newton-Leibniz formula.
9. Improper integral. Application of integrals.
10. Sequences and their limits.
11. Rows, criteria of convergence.
12. Introduction to differential equations.
13. Other topics of mathematical analysis.

Literature:

[1] J. Stewart, Single variable calculus, Seventh Edition, Brooks/Cole, 2012, ISBN 0538497831.

Requirements:

See web page.

Keywords:

limits, derivatives, integrals, series

Subject is included into these academic programs:

Program Branch Role Recommended semester
BPKYR_2021 Common courses P 1
BPEK_2016 Common courses P 1
BPOI1_2016 Computer and Information Science P 2
BPOI_BO_2016 Common courses P 2
BPOI4_2016 Computer Games and Graphics P 2
BPOI3_2016 Software P 2
BPOI2_2016 Internet of Things P 2
BPOI_BO_2018 Common courses P 2
BPOI4_2018 Computer Games and Graphics P 2
BPOI3_2018 Software P 2
BPOI2_2018 Internet of Things P 2
BPOI1_2018 Artificial Intelligence and Computer Science P 2
BPOI_BO_2025 Common courses P 2
BPOI4_2025 Computer Games and Graphics P 2
BPOI3_2025 Software P 2
BPOI2_2025 Internet of Things P 2
BPOI1_2025 Artificial Intelligence and Computer Science P 2
BPKYR_2016 Common courses P 1
BPEEM1_2016 Applied Electrical Engineering P 1
BPEEM_BO_2016 Common courses P 1
BPEEM2_2016 Electrical Engineering and Management P 1

Page updated 12.5.2026 17:51:59, semester: L/2029-30, Z/2025-6, Z/2026-7, L/2025-6, L/2026-7, Z,L/2027-8, Z,L/2028-9, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)
Responsible person: prof. Ing. Jiří Jakovenko, Ph.D.